Tensor products of bimodules over monoids

TL;DR

This paper extends the tensor product concept to bimodules over monoids and hyperrings, ensuring functoriality and analyzing morphisms, thus broadening the algebraic framework for modules over generalized algebraic structures.

Contribution

It introduces a modified tensor product for bimodules over monoids and hyperrings, addressing functoriality and morphism types, expanding algebraic tools for these structures.

Findings

Tensor product adapted for hyperrings and bimodules

Functoriality of tensor product of residue hypermodules

Analysis of morphisms in the context of hyperrings

Abstract

We modify the well-known tensor product of modules over a semiring, in order to treat modules over hyperrings, and, more generally, for bimodules (and bimagmas) over monoids. The tensor product of residue hypermodules is functorial. Special attention is paid to different kinds of morphisms and the work of Nakamura and Reyes.